modeling and application of electromagnetic and thermal ...978-981-15-0173-9/1.pdf · and thermal...

Modeling and Application of Electromagneticand Thermal Field in Electrical Engineering

Zhiguang Cheng • Norio Takahashi •

Behzad ForghaniEditors

Modeling and Applicationof Electromagneticand Thermal Fieldin Electrical Engineering

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EditorsZhiguang ChengInstitute of Power Transmissionand Transformation TechnologyBaobian Electric Co., Ltd.Baoding, Hebei, China

Norio Takahashi (deceased)Okayama, Japan

Behzad ForghaniMentor Infolytica, a Siemens BusinessMontreal, QC, Canada

ISBN 978-981-15-0172-2 ISBN 978-981-15-0173-9 (eBook)https://doi.org/10.1007/978-981-15-0173-9

Jointly published with Science PressThe print edition is not for sale in China Mainland. Customers from China Mainland please order theprint book from: Science Press.

© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2020This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publishers, the authors, and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publishers nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made. The publishers remain neutral with regard tojurisdictional claims in published maps and institutional affiliations.

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https://doi.org/10.1007/978-981-15-0173-9

Foreword

The distribution and use of electrical energy is fundamental to the functioning ofmodern society. From the discovery of electromagnetic energy around 200 yearsago to the present, devices based on converting energy between electromagnetic,mechanical and thermal forms have become so prevalent that they are hardly givena second thought and yet every one of those devices from large industrialmachinery; through land, air and sea transportation to domestic devices rangingfrom washing machines to stoves, has to be designed, manufactured and tested. Inaddition, a generation and distribution system for electrical energy which is reliable,robust and efficient, has to be constructed. In 2017, about 26,000 TWh of electricalenergy was generated, distributed and used globally. To minimize the losses in thetransmission and distribution system and reduce the costs of the infrastructure,electrical energy is usually transmitted at a very high voltage, while it is generatedand used at significantly lower levels. This implies the need for devices capable ofchanging voltages, i.e. transformers. It is interesting to consider that every Wh ofelectrical energy delivered through the distribution system and subsequently usedhas passed through at least two and probably nearer to ten, transformers.

From the very beginning of the electromagnetic era, the need for design tools hasbeen paramount. Building physical prototypes is prohibitively expensive both in thecost of each prototype and in the time taken to realize a final device. Simple designtools based more on experience than theory evolved relatively quickly in thenineteenth century and the development of electromagnetic field theory providedthe explanation of the physics underlying the operation of such devices. In effect,designers from the start have been using whatever tools and representations theycan to create a virtual model of the device to determine the probable performanceand explore the design space. With the advent of digital computers, the possibilityof solving the field equations to simulate the actual performance of a device movedfrom a concept to reality. Over the past half century, both the computing hardwareand the numerical methods necessary for solving the partial differential equationstogether with advanced representations of material properties, etc., have developedto a point where the simulations may now be considered accurate “digital twins”of the physical device allowing, in many cases, more detailed explorations of device

v

performance than is possible on the physical system. These twins not only enablethe total elapsed time from specification to full design to be decreased dramatically(along with a substantial reduction in costs) but also allow for manufacturingquestions to be answered during the construction process and for performancemonitoring during the operation of the physical device to identify developing faultsbefore they become critical. This is a fundamental component of the conceptsinvolved in moving to an “Industry 4.0” based world.

However, there are many requirements placed on the digital twin. First, it mustrepresent the performance of the real device to the level of accuracy needed by thedesigner. This can vary through the design process and, typically, follows the wellknown “V-cycle”, i.e. in the initial phases of a design, a system level representationof the device is needed—sometimes referred to as a Reduced Order Model—whichincorporates as much of the multi-physics operation of the device as possible whileallowing a fast exploration of the design space. This is sometimes referred to as“Front-Loading” the design process. As the design progresses, the simulation needsto become more detailed to answer questions such as the distribution of local lossesin the device, the temperature rise in various components due to the losses, theforces on various components, etc. However, while it is tempting to just buildextremely large models involving millions or tens of millions of degrees of free-dom, the time taken to generate the performance of the twin and to explore thedesign space is critical. To be competitive, it is important that the overall designtime is reduced as much as possible.

From the above discussion, the digital twin of an electromagnetic device shouldinvolve an appropriate numerical representation of the electromagnetic field. Sincethe behaviour of the field is controlled by the magnetic, electric, thermal andstructural performance of the materials used to construct the device, it is crucial thatany simulation system models the properties effectively. In addition, because all theareas of physics—magnetics, thermal, structural—are linked through the materials,a valid simulation must include a full multi-physics representation and, because thelosses impact the thermal performance, the most important is an effectivemagnetic-thermal representation of the device. However, the behavior of the fieldalso impacts the construction. For example, reducing losses in ferromagneticcomponents leads to a need to laminate the cores carrying the magnetic fluxes.These laminations are usually sub-millimeter in thickness while the dimensionsof the entire device may often be measured in meters. The issues of scale can lead tohuge numerical systems if all the details of the device are modeled accurately. This,in turn, can lead to extremely long simulation times. However, by representingsome of the smaller components of the device with compact models, the problemsizes can be reduced significantly with no real loss in accuracy but with a massivegain in simulation speed allowing the digital twin to run on significantly smallerhardware systems.

This book provides an overview of the state-of-the-art for many of the issuesdescribed earlier. It has been created by authors who have significant experience ineach of the areas critical to constructing and verifying the validity of a digital twin.They are recognized international authorities in each of their areas and several have

vi Foreword

been involved in organizations such as the International Compumag Society, theIEEE and standards organizations. They have made fundamental contributions tothe representation and solution of electromagnetic field problems, the accuratemodeling of materials, the measurement of material properties under the actualoperating conditions experienced within a device, the construction of simulationsystems, the development of verification and validation models for software and thedevelopment of optimization processes for an effective search of the design space.The book has been edited by three internationally recognized experts in the field:Dr. Zhiguang Cheng who has decades of experience in electromagnetic analysis,the validation of modeling and simulation tools, the measurement and prediction ofmaterial properties and, together with a large research and development team, hasbeen involved in developing some of the world’s largest transformers (withBaobian Electric, China); Prof. Norio Takahashi (from Okayama University,Japan), who received the Nikola Tesla award from the IEEE in 2013 for his work inmodeling and design of electrical machines and was one of the leading developersof numerical formulations of electromagnetic field problems as well as havingconsiderable expertise in material modeling; and Mr. Behzad Forghani who hasbeen involved in the development of industrial software tools for electromagneticsdesign since the early 1980’s (with Infolytica, Canada—now Mentor-Infolytica, ASiemens Business) and has been a member of the International Compumag SocietyBoard for more than two decades. The resulting text represents man-centuries ofexperience in efficient modeling, numerical simulation and experimental verifica-tion of the complex engineering problems encountered in real electromagneticdevices and explains and identifies the issues that are crucial to anyone developingor using digital twin representations of such systems.

Although the contents have been created with the transformer designer in mind,much applies to almost any low frequency electromagnetic device. The initialchapters in the first part discuss the most often used approaches taken to developinga numerical representation of the magnetic field. The issues and advantages of eachapproach are discussed, and the reader is provided both with the theoreticaldevelopment and with computational experiments which demonstrate the effec-tiveness of the approaches in terms of the problem sizes and typical solution times.While the representations deal with the basic field equations, constructing aneffective system requires the introduction of knowledge and understanding tominimize the problem sizes without sacrificing accuracy. Thus, the next sectionsdeal with issues which are of engineering importance, including optimizationprocesses for exploring the design space. The theme here is very much “how can wedevelop an effective design tool?”. This highlights the needs of the practicingdesigner of both speed of simulation and accuracy of solution. However, theimportance of linking the thermal and magnetic field calculations is stressed and, inmany devices, it is the thermal impact of the magnetic field that causes some of themost severe design issues and leads to many of the engineering problems whichmust be solved. The culmination of these discussions is demonstrated by thesimulation system, “SimcenterTM MAGNETTM”. This is an example of a com-mercial tool that implements many of the concepts discussed previously. However,

Foreword vii

no tool can provide for every possibility that a designer wants so the ability todevelop customizations, or shells, shows how the power of the digital twin can beleveraged for specific performance requirements. Finally, recognizing that thetransient performance of devices is becoming ever more important, an approach foraccelerating these computations is discussed.

Possibly the most interesting component of this book is the detailed review ofmaterial properties and their modeling. Material properties dominate in the solutionof field problems and an understanding of the issues involved, from the behaviourunder non-sinusoidal conditions, in the presence of dc bias and with rotationalfluxes, to the impact of temperature on the behavior is critical in developing aneffective and accurate simulation. An understanding of the properties and theirvariances can also help an engineer to understand what levels of accuracy it makessense to request from the system. This section of the book draws on expertise inmaterial property and measurement which is second to none in the world. The workof Prof. Norio Takahashi (Okayama, Japan) and Prof. Johannes Sievert(Braunshweig, Germany) is internationally recognized. In addition, the practicalinformation on making measurements, the effect of core structures on propertiesand the design of experimental facilities, based on industrial experience, is extre-mely valuable in understanding what can realistically be done. This work is verytimely—it deals with issues that are arising because of geomagnetically inducedcurrents (a problem that all transformers must now be designed to survive),renewable energy systems, such as wind generation, that create huge time varyingeffects and high voltage dc (HVDC) transmission systems. If for no other reason,this book stands out in the way it discusses the issues with material performance ina real device.

Notwithstanding the above, no digital twin is acceptable unless its performancehas been validated and verified. The authors of this book have been involved, forabout two decades, with the development of a series of variations of an interna-tionally accepted test model for software performance validation. The model,TEAM problem 21, includes many of the basic features found in a large powertransformer and the experimental version of the problem has been built, and itsperformance modeled and measured, as co-research projects, jointly organized byZhiguang Cheng, Norio Takahashi and Behzad Forghani.

While much of the information provided in the book is of general use to anyoneworking on the design of low frequency electromagnetic devices, the last part dealsspecifically with issues encountered in large modern power transformers expectedto operate within the new grid architectures that are being proposed. The experienceand knowledge embedded here is likely to be immensely valuable to anyoneinvolved in transformer design to meet current operational requirements andinternational standards.

Overall, this work is an extremely comprehensive review of issues encounteredin the design process for electromagnetic devices. It is a book which is targeted atboth the research engineer and the practicing designer who want to understand thebasis and capabilities of modern simulation systems for electromagnetics. The bookcontains knowledge and information from experts in the field developed over

viii Foreword

decades of both research work and practical experience. With over 450 references,the book contains one of the most comprehensive lists available of the key publi-cations in the area of electromagnetic-thermal modeling and provides the readerwith the opportunity to dig deeper into each of the areas covered.

David A. LowtherPh.D., A.K.C., C.Eng.(UK), P.Eng. (Ont), F.I.E.T., F.C.A.E., F.I.E.E.E.

Professor of Electrical EngineeringDepartment of Electrical and Computer Engineering

McGill UniversityMontreal, QC, Canada

e-mail: [email protected]

Foreword ix

mailto:[email protected]

Preface

The co-research of the authors of this book, mainly involving 3-D electromagneticand thermal modeling and simulation, measurement and prediction of materialproperties under standard and non-standard operating conditions, engineering-oriented benchmarking, based on well-established and collaborative research plat-forms, and transformer-related industrial applications, goes back to 30 years ago.This co-publication is based on its former version published in 2009, but is con-siderably extended, including the authors’ major recent co-research works.

Motivation

The unprecedented high voltage and high capacity of today’s electrical equipment,the economic pressures, as well as considerations, such as, the environmentalprotection, and high reliability within the life cycle, increasingly impose new andstringent requirements for the efficient and accurate analysis and design techniques,in particular with regards to the simulation of electromagnetic and thermal behavior,in large electromagnetic devices.

Modeling and prediction of the electromagnetic and thermal field behavior oflarge electrical equipment, especially in the UHV transmission and transformationengineering, lay the foundation for the in-depth study of topics, such as, vibrationand noise, heating and cooling effects, under actual operating conditions. It involvesmaterial property modeling, large-scale multi-physics, multi-scale numerical anal-ysis under complex conditions, and validation based on benchmark models,product-level models, and/or experiments with actual products.

This book aims to report the research works related to the above key projects,including many valuable measurement and simulation results, to motivate researchteams to promote and participate in cooperation and exchanges in these fields, andto stimulate the exploration and discussion on future challenging topics.

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Outline of This Book

This book focuses on the engineering electromagnetic and thermal field modelingand the related applications, taking large power transformers as its industrialbackground, and consists of the following five main parts:

(1) An overview of the electromagnetic and thermal field problems in electro-magnetic devices, the new challenges posed by the UHV transformer engi-neering, the key research projects, and the foundation of the finite elementmethod;

(2) The key technologies in solving the electromagnetic and thermal field prob-lems, the effective solution of coupled electromagnetic and thermal fields, theAPI-based customized scripts, and the efficient harmonic balance finite elementmethod;

(3) The foundation of the material property modeling, the improvement of classicalmagnetic measurement methods, the experimental study on magnetic aniso-tropy of grain-oriented silicon steel, the electromagnetic properties modelingbased on product-level core models, the measurement and modeling of rotatingmagnetic properties, and the magnetic measurements of materials and com-ponents under complex conditions;

(4) The establishment and development of the engineering-oriented BenchmarkFamily (P21), the research on the additional core loss, caused by 3-D leakagemagnetic flux, and the validation of engineering effectiveness of its analysismethod and software;

(5) The engineering-oriented application research, including the modeling andsimulation of product-based magnetic-thermal coupling, the transformer DCbias, and the heating and cooling behavior.

Co-authorship and Edition

This book is the result of long-term collaboration of an international R&D teamcomposed of members from the Institute of Power Transmission andTransformation Technology, Baobian Electric, China; State Key Laboratory ofReliability and Intelligence of Electrical Equipment, Hebei University ofTechnology, China; Department of Electrical Engineering, North China ElectricPower University, China; Department of Electrical and Electronic Engineering,Okayama University, Japan; Mentor-Infolytica, a Siemens Business, Montreal,Canada; and Physikalisch-Technische Bundesanstalt, IEC Technical Committee,Magnetic Alloys and Steels, Germany.

The Co-authorship

Herein, the co-authors of all 16 Chapters are: Chap. 1: Zhiguang Cheng; Chap. 2:Zhiguang Cheng and Norio Takahashi; Chap. 3: Norio Takahashi; Chap. 4:

xii Preface

Behzad Forghani; Chap. 5: Junjie Zhang; Chap. 6: Xiaojun Zhao; Chap. 7: NorioTakahashi; Chap. 8: Zhiguang Cheng, Lianbin Shi, and Johannes Sievert; Chap. 9:Tao Liu; Chap. 10: Yongjian Li; Chap. 11: Zhenbin Du, Meilin Lu, and Fulai Che;Chap. 12: Zhiguang Cheng, Norio Takahashi, Behzad Forghani, and Lanrong Liu;Chap. 13: Zhiguang Cheng, Chen Chang, and Dongjie Wang; Chap. 14: LanrongLiu, Jie Li, and Fulai Che; Chap. 15: Mansheng Guo; Chap. 16: Weige Wu andGang Liu.

Edition and Review

A number of illustrated figures and tables of the book were compiled and updatedby Chen Chang and Lianbin Shi. Dongjie Wang organized the English edition. TheEnglish text for the illustrations in Chaps. 3 and 7 was edited by Meilin Lu.

Sajid Hussain and Dexin Xie were invited to review the manuscripts. All theauthors contributed to the review process and the editorial work.

The final compilation, review, and edits of all the manuscripts of the book wereperformed by Zhiguang Cheng, Behzad Forghani, Yongjian Li, and Xiaojun Zhao.

The Authors’ Expectations

This book is intended to be helpful to engineers, researchers, and postgraduatestudents majoring in electrical engineering, with an emphasis on efficientelectromagnetic-thermal analysis methods, accurate material properties modeling,rigorous validation of the effectiveness of numerical modeling and simulation, andthorough considerations and discussions on the future research projects, e.g., themodeling and simulation of coupled electromagnetic-thermal-fluid fields, andcoupled electromagnetic-vibration-noise fields. The authors are grateful for all thecomments, suggestions, and discussions on this book, which will be very helpfulfor further co-research.

Baoding, China Zhiguang ChengMontreal, Canada Behzad ForghaniJune 2019

Preface xiii

Acknowledgements

The publication of this book was supported by all the related leaderships of boththe Baobian Electric and Institute of Power Transmission and TransformationTechnology, by the Hebei Key Laboratory of Electromagnetic & StructuralPerformance of Power Transmission and Transformation Equipment, and by theState Key Laboratory of Reliability and Intelligence of Electrical Equipment, HebeiUniversity of Technology, China.

The related research works of this book were funded in part by the NaturalScience Foundation of China under grants no. 59277296, no. 59924035, no.51237005, and no. 50777042, by the joint project of the Chinese Academy ofSciences and National Natural Science Foundation of China under grantXK2018JSC001, by the National Key R&D Program of China under grant2016YFB0300300, by the State Grid Science and Technology Projects undergrant SGRI-WD-71-13-002, and by the Hebei Provincial Government SpecialTalents Training Funds.

In this book, a number of electromagnetic and thermal field simulations wereperformed, based on the jointly established industrial application center, usingSimcenterTM MAGNETTM software. Simcenter, MAGNET and SimcenterTM

FLOEFDTM are trademarks or registered trademarks of Siemens Product LifecycleManagement Software Inc., or its subsidiaries or affiliates, in the United States and inother countries. Restricted © Siemens 2019 is the Siemens copyright notice.

Here we are very grateful to all our respected predecessors, mentors, leaders, andexperts in the field for their long-term countless support and help in so many ways.

At this moment, we would like to thank all our colleagues, postdoctoral fellowsand postgraduate students for their contributions to the relevant experimentalstudies and numerical calculations in this book, over the years.

We are grateful to Ms. Hongmei Liu of Science Press (Beijing) and Ms. JingDou of Springer Beijing Office for their support and cooperation.

In particular, we wish to dedicate this book to Norio Takahashi, our co-editorand author. We are very sad that he deceased young, and will always remember hisgreat cooperation and outstanding contribution to the field.

Finally, we are deeply grateful to all supporters and collaborators in ourco-research throughout the decades.

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Contents

Part I Engineering Electromagnetic and Thermal Field Problemsand FEM Fundamentals

1 General Survey of Engineering Electromagnetic and ThermalField Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Zhiguang Cheng1.1 Overview of Engineering Electromagnetic and Thermal Field

Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 New Challenges Posed by UHV Transformer Engineering . . . . 51.3 Some Key Research Projects . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.1 Accurate Analysis of Total Core Loss . . . . . . . . . . . . 91.3.2 Efficient Solution of Transformer Winding Loss . . . . . 111.3.3 Modeling and Control of Stray-Field Loss

in Structural Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.4 Numerical Prediction and Measurement

of Electromagnetic and Thermal Fields . . . . . . . . . . . 121.4 Realization of Accurate Modeling and Simulation

of Electromagnetic and Thermal Performance . . . . . . . . . . . . . . 131.5 Overall Composition of the Book . . . . . . . . . . . . . . . . . . . . . . 16References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Low-Frequency Electromagnetic Fields and Finite ElementMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Zhiguang Cheng and Norio Takahashi2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Governing Equations for Analysis of Low-Frequency Eddy

Current Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4 Ar-V-Ar-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5 Scalar and Vector Galerkin Weight Function . . . . . . . . . . . . . . 28

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2.6 Discussion on Edge Elements . . . . . . . . . . . . . . . . . . . . . . . . . 292.7 Comparison of Basic Equations and Galerkin Residuals

of Nodal Elements and Edge Elements . . . . . . . . . . . . . . . . . . . 312.8 Comparison of Nonzero Entries and Total Unknowns

in Coefficient Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.8.1 Unknowns and Number of Nonzero Entries

in Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.8.2 Comparison of Nonzero Entries and Total

Unknowns in Matrix . . . . . . . . . . . . . . . . . . . . . . . . . 352.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Appendix: Formulation of A-V-A and Galerkin Weighted ResidualProcessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Part II Engineering Electromagnetic and Thermal Field Modeling

3 Some Key Techniques in Electromagnetic and Thermal FieldModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Norio Takahashi3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2 Special Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.1 What Is Special Element? . . . . . . . . . . . . . . . . . . . . . 543.2.2 Distribution of Potentials in Special Elements . . . . . . 553.2.3 Finite Element Formulation . . . . . . . . . . . . . . . . . . . . 573.2.4 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.3 Voltage-Driven Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.3.1 FEM Considering Voltage Source . . . . . . . . . . . . . . . 613.3.2 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Optimal Design Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.4.1 Various Optimization Methods . . . . . . . . . . . . . . . . . 653.4.2 Experimental Design Method (EDM) . . . . . . . . . . . . . 663.4.3 Rosenbrock’s Method (RBM) . . . . . . . . . . . . . . . . . . 683.4.4 Evolution Strategy (ES) . . . . . . . . . . . . . . . . . . . . . . 703.4.5 ON/OFF Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.4.6 Example of Application . . . . . . . . . . . . . . . . . . . . . . 75

3.5 Magneto-Thermal Coupled Analysis . . . . . . . . . . . . . . . . . . . . 863.5.1 Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.5.2 Magneto-Thermal Analysis . . . . . . . . . . . . . . . . . . . . 883.5.3 Magneto-Thermal-Fluid Analysis . . . . . . . . . . . . . . . . 90

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

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4 Solution of Coupled Electromagnetic and Thermal Fields . . . . . . . 101Behzad Forghani4.1 Simulation as a Design and Analysis Tool . . . . . . . . . . . . . . . . 1024.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2.2 Coils and Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.2.3 Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.2.4 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.2.5 Material Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.2.6 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 1124.2.7 Accuracy Considerations . . . . . . . . . . . . . . . . . . . . . . 114

4.3 Result Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.3.1 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.3.2 Global Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.3.3 Scripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.4 Electromagnetic Field Computation . . . . . . . . . . . . . . . . . . . . . 1264.4.1 Solving the Electromagnetic Field Problem . . . . . . . . 1264.4.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 1284.4.3 Problem Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1284.4.4 Surface Impedance Modeling . . . . . . . . . . . . . . . . . . 1294.4.5 Skin Depth Modeling . . . . . . . . . . . . . . . . . . . . . . . . 131

4.5 Temperature Field Computation . . . . . . . . . . . . . . . . . . . . . . . . 1314.5.1 Solving the Thermal Field Problem . . . . . . . . . . . . . . 1314.5.2 Problem Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.6 Mechanism of Coupling Electromagnetic and Thermal FieldSolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.6.1 Sources of Heat Generation . . . . . . . . . . . . . . . . . . . . 1324.6.2 Solving the Coupled Electromagnetic–Thermal

Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1334.6.3 Coupled Solution Controls . . . . . . . . . . . . . . . . . . . . 1344.6.4 Coupled Electromagnetic–Thermal–Flow

Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5 Development of Customized Scripts . . . . . . . . . . . . . . . . . . . . . . . . 139Junjie Zhang5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.2 Basics of the Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.2.1 Definition and Role of the Script . . . . . . . . . . . . . . . . 1415.2.2 Classification of the Script . . . . . . . . . . . . . . . . . . . . 1415.2.3 Concise Basic Syntax of VBScript . . . . . . . . . . . . . . 142

Contents xix

5.3 Script Development in Simcenter MAGNET . . . . . . . . . . . . . . 1555.3.1 Automatic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 1555.3.2 Recording Script File . . . . . . . . . . . . . . . . . . . . . . . . 1595.3.3 Interoperability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1595.3.4 Export the Field Data . . . . . . . . . . . . . . . . . . . . . . . . 163

5.4 Development of a Script for Transformer Winding ParametersCalculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645.4.1 Requirements for Script to Calculate Transformer

Winding Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 1645.4.2 Goal of the Script Used to Calculate Transformer

Winding Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 1655.4.3 FEM Method to Calculate the Eddy Loss

of Windings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.4.4 Implementation Process . . . . . . . . . . . . . . . . . . . . . . 167


6 Harmonic-Balanced Finite Element Methodand Its Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Xiaojun Zhao6.1 Development of HBFEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.1.1 Basic Theory of HBFEM . . . . . . . . . . . . . . . . . . . . . 1766.1.2 Coupling Between Electric Circuits and the

Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1776.1.3 Epstein Frame-like Core Model Under DC-Biased

Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.1.4 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . 180

6.2 The Fixed-Point Harmonic-Balanced Method . . . . . . . . . . . . . . 1916.2.1 The Fixed-Point Technique . . . . . . . . . . . . . . . . . . . . 1926.2.2 Fixed-Point Harmonic-Balanced Equation . . . . . . . . . 1926.2.3 Electromagnetic Coupling . . . . . . . . . . . . . . . . . . . . . 1946.2.4 Validation and Discussion . . . . . . . . . . . . . . . . . . . . . 197

6.3 Decomposed Harmonic-Balanced Method . . . . . . . . . . . . . . . . 1996.3.1 The Fixed-Point Reluctivity . . . . . . . . . . . . . . . . . . . 1996.3.2 Linearization and Decomposition . . . . . . . . . . . . . . . . 1996.3.3 Force Computation of a Gapped Reactor Core

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

xx Contents

Part III Measurement and Modeling of Magnetic Materialand Component Properties

7 Fundamentals of Magnetic Material Modeling . . . . . . . . . . . . . . . . 213Norio Takahashi7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2147.2 Modeling of B–H Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

7.2.1 Relationship Between B and H . . . . . . . . . . . . . . . . . 2147.2.2 Sectional Polynomial Approximation . . . . . . . . . . . . . 2157.2.3 Approximation of B–H Curve at High

Flux Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2177.3 Modeling of Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . 218

7.3.1 Problem of Two B–H Curves Model . . . . . . . . . . . . . 2187.3.2 Multi-B–H Curve Model . . . . . . . . . . . . . . . . . . . . . . 2207.3.3 E&SS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

7.4 Hysteresis Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2297.4.1 Various Hysteresis Models . . . . . . . . . . . . . . . . . . . . 2297.4.2 Interpolation Method . . . . . . . . . . . . . . . . . . . . . . . . 2307.4.3 Preisach Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2327.4.4 Jiles–Atherton Model . . . . . . . . . . . . . . . . . . . . . . . . 2377.4.5 Stoner–Wohlfarth Model . . . . . . . . . . . . . . . . . . . . . . 2397.4.6 Effect of Hysteresis on Flux Distribution

of Single-Phase Transformer . . . . . . . . . . . . . . . . . . . 2437.5 Estimation of Iron Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

7.5.1 Iron Loss Under Alternating Flux . . . . . . . . . . . . . . . 2447.5.2 Iron Loss Under Rotating Flux . . . . . . . . . . . . . . . . . 247

7.6 Modeling of Laminated Core . . . . . . . . . . . . . . . . . . . . . . . . . . 2507.6.1 Laminated Core and Various Modeling Methods . . . . 2507.6.2 Homogenization Method . . . . . . . . . . . . . . . . . . . . . . 2507.6.3 Two-Zone Method . . . . . . . . . . . . . . . . . . . . . . . . . . 251

7.7 Factors Affecting Magnetic Properties of Electrical Steel . . . . . . 2577.7.1 Residual Stress by Cutting . . . . . . . . . . . . . . . . . . . . 2577.7.2 Compressive Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 2597.7.3 Effect of Press and Shrink Fitting on Iron Loss

of Motor Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2607.7.4 Iron Loss Under Rotating Flux Excitation . . . . . . . . . 2627.7.5 Iron Loss Under DC Bias Excitation . . . . . . . . . . . . . 264


8 Magnetic Measurement Based on Epstein Combinationand Multi-angle Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Zhiguang Cheng, Lianbin Shi and Johannes Sievert8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Contents xxi

8.2 Magnetic Properties Under Rotating Flux Conditions . . . . . . . . 2738.3 Application and Improvement of Epstein Frame

Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2758.3.1 Epstein Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2758.3.2 Epstein Combination and Loss Data-Based

Weighted Processing Method . . . . . . . . . . . . . . . . . . 2778.4 Magnetic Measurement Based on Multi-angle Sampling . . . . . . 281

8.4.1 Multi-direction Magnetic Measurement . . . . . . . . . . . 2818.4.2 Multi-angle Sampling . . . . . . . . . . . . . . . . . . . . . . . . 281

8.5 Measurement Results and Discussions . . . . . . . . . . . . . . . . . . . 2838.5.1 Bm–Hm Curve Before Annealing (30P120) . . . . . . . . . 2838.5.2 Bm–Wt Curve Before Annealing (30P120) . . . . . . . . . 2858.5.3 Comparison of Bm–Hm Curves Measured Before

and After Annealing . . . . . . . . . . . . . . . . . . . . . . . . . 2858.5.4 Comparison of Bm–Wt Curves Measured Before

and After Annealing . . . . . . . . . . . . . . . . . . . . . . . . . 2868.6 Measuring Record of Voltage Starting Distortion in Magnetic

Measurement Before and After Sample-Annealing . . . . . . . . . . 2938.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

9 Electromagnetic Property Modeling Based on Product-LevelCore Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299Tao Liu9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3009.2 Measurement of Magnetic Properties of Product-Level Core

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3019.2.1 Two-Laminated Core Models . . . . . . . . . . . . . . . . . . 3019.2.2 Experimental Equipment . . . . . . . . . . . . . . . . . . . . . . 3019.2.3 Experimental Content and Circuit . . . . . . . . . . . . . . . 3029.2.4 Measurement Procedure and Key Points . . . . . . . . . . 302

9.3 Measurement Results of Magnetic Properties of Product-LevelCore Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3089.3.1 Waveforms of Exciting Current and Voltage . . . . . . . 3089.3.2 Experimental Data of Core Models . . . . . . . . . . . . . . 3089.3.3 Magnetic Properties of Core Models and

Comparison with Material Properties . . . . . . . . . . . . . 3119.4 Separation of Exciting Power and Active Power Loss

in the Joint Area and Middle Uniform Area of the Core . . . . . . 3129.4.1 Separation of Exciting Power . . . . . . . . . . . . . . . . . . 3129.4.2 Separation of the Active Power Loss . . . . . . . . . . . . . 317

9.5 Specific Total Loss Calculation of the Middle Uniform Areawith Two-Core Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

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9.6 Determination of Building Factor of Core Model . . . . . . . . . . . 3219.7 Research on Magnetic Measurement of Transformer Core

at Different Ambient Temperatures . . . . . . . . . . . . . . . . . . . . . 3249.7.1 Experimental Setup and Process . . . . . . . . . . . . . . . . 3259.7.2 Measurement Results and Analysis . . . . . . . . . . . . . . 326

9.8 Magnetic Properties Modeling Based on Ring Cores Beforeand After Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3349.8.1 Ring Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3349.8.2 Annealing Conditions . . . . . . . . . . . . . . . . . . . . . . . . 3359.8.3 Experimental Result . . . . . . . . . . . . . . . . . . . . . . . . . 335

9.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3399.9.1 Separation of Exciting Power and Magnetic Loss

Based on Laminated Core Models . . . . . . . . . . . . . . . 3399.9.2 Effect of Temperature on the Magnetic Properties . . . 339

Appendix 9.1: Magnetic Property Curves of the Ring Core Beforeand After Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

10 Rotational Magnetic Properties Measurement and Modeling . . . . . 345Yongjian Li10.1 Development of Rotational Magnetic Properties

Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34510.1.1 Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . 34610.1.2 Measurement Apparatus in Field-Metric Method . . . . 34710.1.3 Techniques for Measuring B and H in Field-Metric

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34810.1.4 3-D Magnetic Testing System . . . . . . . . . . . . . . . . . . 35010.1.5 B–H Combined Sensing Structure . . . . . . . . . . . . . . . 35610.1.6 Calibration and Compensation of the 3-D Tester . . . . 357

10.2 Measurement and Analysis of the Rotational MagneticProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36010.2.1 Magnetic Properties of the Soft Magnetic Composite

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36010.2.2 Magnetic Properties of the Silicon Steels . . . . . . . . . . 366

10.3 Vector Hysteresis Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37110.3.1 Definition of the Vector Hysteron . . . . . . . . . . . . . . . 37210.3.2 Modeling of the Vector Hysteresis

Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37610.3.3 Magnetic Properties Prediction and Validation . . . . . . 380


Contents xxiii

11 Measurement and Prediction of Magnetic Property of GO SiliconSteel Under Non-standard Excitation Conditions . . . . . . . . . . . . . . 389Zhenbin Du, Meilin Lu and Fulai Che11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39011.2 1-D Magnetic Measurement Under Non-standard

Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39011.2.1 Measurement of Magnetic Loss Under Harmonic

or DC-Bias Condition . . . . . . . . . . . . . . . . . . . . . . . . 39111.2.2 Measurement of Magnetic Loss Under Harmonic

and DC-Bias Condition . . . . . . . . . . . . . . . . . . . . . . . 39311.2.3 Measurement of Magnetization Property . . . . . . . . . . 39711.2.4 Measurement of B–H Loop Under Harmonic

and DC-Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39811.3 Magnetic Measurement Under Non-standard Conditions

Based on an Integrated Magnetic Measure-Bench . . . . . . . . . . . 39811.3.1 Magnetic Property Measure-Bench and Two Core

Model Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39811.3.2 Harmonic Excitation . . . . . . . . . . . . . . . . . . . . . . . . . 40111.3.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . 40211.3.4 Specific Total Loss (Model (C70–C50)) . . . . . . . . . . . 40811.3.5 Comparisons Among Specific Total Losses

Measured by Two Core Models . . . . . . . . . . . . . . . . 40911.3.6 Comparison of Specific Total Loss Results

(Using Core Models and Epstein Frame) . . . . . . . . . . 41211.3.7 Exciting Power Inside Laminated Core . . . . . . . . . . . 41211.3.8 Remarks 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

11.4 Measurement and Numerical Analysis of Magnetic LossUnder AC–DC Hybrid Excitation . . . . . . . . . . . . . . . . . . . . . . 41811.4.1 Core Model Used for Magnetic Measurement Under

Harmonic and DC-Bias Excitations . . . . . . . . . . . . . . 41811.4.2 Feasibility of Magnetic Measurement Based on the

New Core Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 42111.4.3 Numerical Calculation and Validation of Magnetic

Loss Inside Square Laminated Frame Under AC–DCHybrid Excitation Conditions . . . . . . . . . . . . . . . . . . 423

11.4.4 Remarks 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42611.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426Appendix 1 Non-standard Magnetic Measurement Results . . . . . . . . . 427References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

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Part IV Validation Based on a Well-Established BenchmarkingSystem

12 Establishment and Development of Benchmark Family (P21) . . . . . 451Zhiguang Cheng, Norio Takahashi, Behzad Forghaniand Lanrong Liu12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45212.2 Development of TEAM Problem 21 . . . . . . . . . . . . . . . . . . . . 454

12.2.1 Modeling and Prediction of Stray-Field Loss . . . . . . . 45412.2.2 Proposal and Updates to Problem 21 . . . . . . . . . . . . . 455

12.3 Definition of Problem 21 Benchmark Family . . . . . . . . . . . . . . 45812.3.1 Benchmark Models . . . . . . . . . . . . . . . . . . . . . . . . . . 45912.3.2 Benchmark Family Data . . . . . . . . . . . . . . . . . . . . . . 46812.3.3 Field Quantities to Be Calculated . . . . . . . . . . . . . . . 470

12.4 Numerical Analysis and Measurement . . . . . . . . . . . . . . . . . . . 47112.4.1 On Eddy Current Analysis Method . . . . . . . . . . . . . . 47112.4.2 Measurement of Magnetic Flux Density

and Interlinkage Flux at Specified Positions . . . . . . . . 47312.4.3 Indirect Determination of Loss in Conducting

Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47612.4.4 Determination of Upper and Lower Bounds

of Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47712.4.5 Eddy Current Losses in Exciting Coils . . . . . . . . . . . 478

12.5 Typical Calculated and Measured Results . . . . . . . . . . . . . . . . . 47912.5.1 Problem 210 (P210-A and P210-B) . . . . . . . . . . . . . . 47912.5.2 Problem 21a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48112.5.3 Problem 21b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48512.5.4 Problem 21c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48912.5.5 Loss Spectrum of Problem 21 Benchmark Family . . . 491

12.6 Problem 21 in Magnetic Saturation . . . . . . . . . . . . . . . . . . . . . 49412.6.1 Nonlinear Iterative Convergence Process Under

Different Excitation Conditions . . . . . . . . . . . . . . . . . 49412.6.2 Introduction of Magnetic Saturation Factor . . . . . . . . 49512.6.3 Analysis of Quasi-saturation . . . . . . . . . . . . . . . . . . . 497

12.7 Further Co-research for Problem 21 Family . . . . . . . . . . . . . . . 50112.7.1 New Proposal of Problem 21 Family . . . . . . . . . . . . . 50112.7.2 Improved Method to Determine Stray-Field Loss . . . . 502

12.8 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50412.8.1 Summary on Problem 21 Family . . . . . . . . . . . . . . . . 50412.8.2 Outlook on the Future Co-research . . . . . . . . . . . . . . 505

Appendix 12.1: Characteristics of Magnetic Steel Plates Usedin Problem 21 Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506Appendix 12.2: Characteristics of Silicon Steel Sheets Usedin Problem 21 Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

Contents xxv

Appendix 12.3: Reference Data of Problem 21 Family . . . . . . . . . . . . 511References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

13 Analysis and Validation of Additional Iron Loss Basedon Benchmark Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517Zhiguang Cheng, Chen Chang and Dongjie Wang13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51713.2 Model Structure and Design Data . . . . . . . . . . . . . . . . . . . . . . 518

13.2.1 Structure and Dimension of the Models . . . . . . . . . . . 51813.2.2 Locations of the Search Coil . . . . . . . . . . . . . . . . . . . 519

13.3 Experimental Method and Targets . . . . . . . . . . . . . . . . . . . . . . 52113.3.1 Experimental Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 52113.3.2 Measurement Procedure . . . . . . . . . . . . . . . . . . . . . . 522

13.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52413.4.1 Measured Loss Results of P21d-M. . . . . . . . . . . . . . . 52413.4.2 Measured Loss Results of P21d-M2 . . . . . . . . . . . . . . 52413.4.3 Flux Waveforms Obtained by Search Coils

in Models P21d-M and P21d-M2 . . . . . . . . . . . . . . . . 52613.4.4 Average Flux Density Waveforms in the Laminated

Sheets of Models P21d-M and P21d-M2 . . . . . . . . . . 52613.4.5 Determination of Maximum Values of Flux Density

Based on P21d-M and P21d-M2 . . . . . . . . . . . . . . . . 52813.4.6 Remarks on the Measured Results . . . . . . . . . . . . . . . 53113.4.7 3-D Finite Element Computation of Additional Iron

Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53513.4.8 Measured and Calculated Results of Iron Loss

and Magnetic Flux . . . . . . . . . . . . . . . . . . . . . . . . . . 53613.4.9 Comparison Between Waveforms of Measured

and Calculated Flux . . . . . . . . . . . . . . . . . . . . . . . . . 53913.4.10 Measured and Calculated Flux Densities at Specified

Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54313.4.11 Question and Discussion . . . . . . . . . . . . . . . . . . . . . . 544

13.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545Appendix 13.1 Magnetic Loss and Flux Under Different ExcitationPatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

Part V Transformer-Related Electromagnetic and ThermalModeling and Application

14 Electromagnetic and Thermal Modeling Based on Large PowerTransformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553Lanrong Liu, Jie Li and Fulai Che14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

xxvi Contents

14.2 Measurement of Electromagnetic and Thermal Propertiesof Commonly Used Metal Materials . . . . . . . . . . . . . . . . . . . . 55414.2.1 Conductivity Measurement . . . . . . . . . . . . . . . . . . . . 55514.2.2 Measurement of DC Magnetization Curve

of Magnetic Steel Plate . . . . . . . . . . . . . . . . . . . . . . . 55714.2.3 Surface Heat Transfer Coefficient of Steel Plate . . . . . 558

14.3 Validation of Modeling and Simulation of Loss and SurfaceHot-Spot Temperature of Steel Plate . . . . . . . . . . . . . . . . . . . . 56214.3.1 Test Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56414.3.2 Measuring System . . . . . . . . . . . . . . . . . . . . . . . . . . 56414.3.3 Results and Validation . . . . . . . . . . . . . . . . . . . . . . . 564

14.4 3-D FE Model for Simulating TransformerComponent Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56914.4.1 3-D Mesh for Magnetic Steel Plate . . . . . . . . . . . . . . 56914.4.2 3-D Mesh for Non-magnetic Steel Plate . . . . . . . . . . . 573

14.5 Engineering Application of Electromagnetic and ThermalSimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57614.5.1 Large Single-Phase Autotransformer

(700 MVA/750 KV) . . . . . . . . . . . . . . . . . . . . . . . . . 57714.5.2 Modeling and Simulation of Preliminary Structural

Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57814.5.3 Thermal Field Simulation of Components in the

Active Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57914.5.4 Modeling and Simulation of Optimized Structures . . . 58114.5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582


15 Engineering-Oriented Modeling and Experimental Researchon DC-Biased Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587Mansheng Guo15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

15.1.1 DC Bias Phenomenon on Power Transformers . . . . . . 58815.1.2 Brief Overview of Investigation on DC-Biased

Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59115.1.3 Key Research Projects . . . . . . . . . . . . . . . . . . . . . . . 593

15.2 Magnetic Properties of Product-Level Laminated Core UnderDC Bias Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59415.2.1 U–I Curve and B−H Curve of Transformer Core . . . . 59415.2.2 Bm – W Curve of Transformer Core . . . . . . . . . . . . . 605

15.3 Calculation of the Exciting Current Under DCBias Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60615.3.1 Principle of Simple Iteration to Determine DC Flux

in Transformer Core . . . . . . . . . . . . . . . . . . . . . . . . . 606

Contents xxvii

15.3.2 Validation of Simple Iteration Method . . . . . . . . . . . . 60815.3.3 Harmonic Analysis of Exciting Current [22] . . . . . . . 613

15.4 Modeling and Computation of Magnetic Field and Loss UnderDC Bias Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61615.4.1 Some Key Factors in Modeling Under DC Bias

Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61615.4.2 Computation of Magnetic Field and Loss Under

No-Load and DC Bias Condition . . . . . . . . . . . . . . . 61815.4.3 Computation of Magnetic Field and Loss Under

Load and DC Bias Condition . . . . . . . . . . . . . . . . . . 62715.4.4 Influence of DC Bias on Loss . . . . . . . . . . . . . . . . . . 634

15.5 The Experimental Research on the DC-Biased 500 KVAutotransformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63615.5.1 No-Load Loss Measurement Under DC Bias

Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63715.5.2 Harmonics Analysis of Exciting Current . . . . . . . . . . 63915.5.3 Measurement of Sound Level Under DC Bias

Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65015.6 On the Ability to Withstand DC Bias for Power

Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65315.7 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657Appendix: Magnetic Property Data Under DC Bias Conditions . . . . . . 659References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

16 Modeling and Validation of Thermal-Fluid Fieldof Transformer Winding Based on a Product-Level Heatingand Cooling Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665Weige Wu and Gang Liu16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66616.2 Test Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66716.3 Experiment Instruments and the Performance . . . . . . . . . . . . . . 67016.4 Measurement Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 67016.5 Numerical Modeling and Simulation of Thermal-Fluid Field

in Transformer Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67216.6 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67616.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

xxviii Contents

About the Editors

Zhiguang Cheng was born in Hebei, China, in 1942.He graduated from Peking University in 1967 andreceived a Ph.D. degree from Tsinghua University in1995. He was a vice chief engineer of the R&D Center,and is currently a research advisor, Baobian Electric.He has received the National and Ministerial Scienceand Technology awards for his contributions to engi-neering science research and application. He is a seniormember, IEEE, and a founding member of theInternational Compumag Society (ICS). His majorinterests are engineering electromagnetic field analysis,benchmarking, magnetic material modeling and indus-trial applications. Over the past decades, he hascooperated with his group to establish the jointindustrial application center, the measurement andprediction system of magnetic material and componentproperties, and the international benchmark family(P21) approved by the ICS.

xxix

Norio Takahashi was born in Hyogo, Japan, in 1951.He received a B.E. degree from Okayama University in1974 and M.E. and Ph.D. degrees from KyotoUniversity in 1976 and 1982, respectively. He was aprofessor of Department of Electrical and ElectronicEngineering, Chair of Electromagnetic DeviceLaboratory of Okayama University, Vice President ofPower and Energy Society, IEE of Japan, VicePresident of International Compumag Society, andIEEE Fellow. His major interests were the developmentof numerical methods for calculating magnetic fieldsand optimal design methods for magnetic devices.Professor Norio Takahashi was deceased, and receivedthe 2013 Nikola Tesla Award for his contributions tofinite element modeling, analysis and optimal designtools of electrical machines, sponsored by the Graingerfoundation and IEEE Power and Energy Society.

Behzad Forghani was born in Tehran, Iran, in 1957.He received a B.Eng. Degree, followed by a M.Eng.degree in 1981, both in Electrical Engineering, fromMcGill University in Montreal, Canada. Since 1981, hehas been working at Infolytica Corporation, and thenMentor Infolytica, a Siemens Business, in the field ofComputational Electromagnetics and is currently aProduct Line Director. He is a senior member, IEEE,and a founding and Board member of the InternationalCompumag Socienty. He is a member of OIQ (Order ofEngineers in Quebec). He regularly serves on theEditorial Boards of Compumag and CEFC (twoconferences with focus on the electromagnetic fieldcomputation). He is a co-author on several peerreviewed papers in the areas of solver formulationand material modeling, as applied to computationalelectromagnetics. In recent years, he has been involvedin statistical analysis and the use of machine learning incancer research, as an affilate member of theDepartments of Diagnostic Radiology and Oncologyat McGill University.

xxx About the Editors

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